1) 3sin²π:2-4tg²π:4-3cos²π:6+3ctg²π:2 2) tg5π:4*sinπ:3-cos7π:6*sin3π:2 3) sinα=3:4,0≤α≤π:2 4) ctgα=2:3,π≤α≤3π:2 5) ctgα-cosα-1:sinα 6) (sinβ*ctgβ) ² + (cosβ*tgβ) 2

1) 3 * sin ² (π : 2) - 4 * tg ² (π : 4) - 3 * cos ² (π : 6) + 3 * ctg ² (π : 2) = 3 * 1 ^ 2 - 4 * 1 ^ 2 - 3 * (√3/2) ^ 2 + 3 * 0 ^ 2 = 3 - 4 - 3 * 3/4 = - 1 - 9/4 = - 4/4 - 9/4 = - 13/4;

2) tg (5 * π : 4) * sin (π : 3) - cos (7 * π : 6) * sin (3 * π : 2) = 1 * √3/2 - (-√3/2) * ( - 1) = √3/2 - √3/2 = 0;

3) sin α = 3 : 4, 0 ≤ α ≤ π : 2;

cos a = √ (1 - sin ^ 2 a) = √ (1 - (3/4) ^ 2) = √ (1 - 9/16) = √16/16 - 9/16) = √ (7/16) = √7/4;

4) ctg α = 2 : 3, π ≤ α ≤ 3 * π : 2;

tg a = 1/ctg a = 1 / (2/3) = 1 * 3/2 = 3/2 = 1,5;

5) ctg α - (cos α - 1) : sin = cos a/sin a - (cos α - 1) : sin = (cos a - (cos a - 1)) / sin a = (cos a - cos a + 1) / sin a = 1/sin a;

6) (sin β * ctg β) ² + (cos β * tgβ) ² = (sin β * cos β/sin β) ² + (cos β * sin β/cosβ) ² = cos ^ 2 β + sin ^ 2 β = 1.